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Jun-Wei Zhu Xin Wang Guang-Hong Yang Fault Estimation for Network Systems via Intermediate Estimator Fault Estimation for Network Systems via Intermediate Estimator · · Jun-Wei Zhu Xin Wang Guang-Hong Yang Fault Estimation for Network Systems via Intermediate Estimator Jun-WeiZhu XinWang InstituteofCyberspaceSecurity HeilongjiangUniversity ZhejiangUniversityofTechnology Harbin,Heilongjiang,China Hangzhou,China Guang-HongYang CollegeofInformationScience andEngineering NortheasternUniversity Shenyang,China ISBN 978-981-19-6320-9 ISBN 978-981-19-6321-6 (eBook) https://doi.org/10.1007/978-981-19-6321-6 ©SpringerNatureSingaporePteLtd.2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface Becauseasmallfaultintheactualsystemmaycausehugeconsequences,theresearch onthesafetyandreliabilityofcomplexdynamicsystemshasbecomeanextremely importanttopic.Inthiscontext,faultestimationtechnologyhasgraduallydeveloped andbecomeoneofthepopularareasinthecontrolfield.Asweknow,faultdetection andisolationtechniquesaimtodeterminewhenandwherethefaultsoccur.Unlike them,faultestimation(FE)techniqueseekstoobtainmorespecificfault’sdynamics online.Comparedwithfaultdetectionandisolation,FEcanobtainmoreinformation ofthefault.Generally,FEisachievedbydesigninganobserver.Sofar,avarietyof different fault observer design methods have appeared, and each method is based ondifferentideas,sotheyhavedifferentcharacteristics.However,therequirements of FE are normally stricter, and there are relatively more constraints. Therefore, there are still a number of challenging issues in FE problems, which greatly limit theapplicationscopeoftheexistingapproaches.Inthisbook,wemainlystudythe problemofFEfornetworksystemsincludingnetworkedsinglesystem,multi-agent system(MAS),andlarge-scaleinterconnectedsystem.Anoveltypeoffaultobserver calledIntermediateEstimator(IE)isproposedforLipschitziannonlinearsystem,and aseriesofmodifiedIEsfornetworksystemsarealsopresented.Moreover,thefault tolerantcontrol(FTC)problemfornetworksystemsisalsostudied. InChap.1,themotivationandhistoryoftheresearchandanoverviewonrecent developmentofFEandFTCarepresented. InChap.2,anewfaultobserverdesignmethod,i.e.,IEisproposedforaclassof Lipschitziannonlinearsystems.Thisobserverhassignificantlyimprovedthetradi- tionaladaptiveobserver(AO),itovercomestheimportantconstraintthatthetradi- tionalAOmustsatisfySPRcondition.Comparedwithothertypesofobservers,this newtypeoffaultobserverhassomeimportantadvantages,e.g.,(a)itdoesnotneed tomeettheobservermatchingconditions,(b)theconvergencespeedoftheFEcan be set and an explicit upper bound of the FE error can be obtained, (c) the norm upper bounds of the fault itself and the first derivative of the fault do not need to beknown,(d)thesystemmatrixisalsonotrequiredtosatisfytheuppertriangular structureconstraint. v vi Preface In Chap. 3, the observer-based fault accommodation (FA) problem for linear systemswithstateperturbationsandmeasurementerrorsisinvestigated.AnovelIE isproposedtoestimatethestateandthefaultssimultaneously,wheretheeffectofstate perturbations and measurement errors is effectively eliminated by fully exploiting thedesignfreedomofsomespecifiedparameters.Basedontheestimation,anFTC schemeissynthesized.Itisprovedthatthestatesoftheresultingclosedloopsystem areuniformlyultimatelyboundedwithanexplicitbound. In Chap. 4, the FA problem for linear systems with time-varying delay, system uncertaintiesandexternaldisturbancesisstudied.AnovelIE-basedFTCschemeis proposed,whereanIEisconstructedtoestimatethestatesandthefaultssimultane- ously,basedontheestimation,anFTCcompensationschemeisdesignedtomitigate theeffectsoffaults,systemuncertaintiesandtime-varyingdelay. In Chap. 5, the robust distributed FE problem is considered for a network of dynamicalsystemswithexternaldisturbances.Basedonlocaloutputmeasurements andstateestimatesfromneighbors,adistributedIEisconstructedforeachnode.By spectraldecompositionoftheLaplacianandproperscalingofthefaultsandthedistur- bances,aspecially-structuredglobalerrorsystemcanbecreated.Itisprovedthatthe statesoftheglobalerrorsystemareuniformlyultimatelyboundedwithanexplicit error bound. The robustness of the global error system can be ensured by directly adjusting the design parameters of the IEs, without introducing any performance specification. InChap.6,westudytheobserver-basedfaulttoleranttrackingcontrolproblemfor linearMASswithmultiplefaultsandmismatcheddisturbances.Anoveldistributed IE-basedfaulttoleranttrackingprotocolispresented.Theleader’sinputisnonzero andunavailabletothefollowers.Byapplyingaprojectiontechnique,themismatched disturbancesaredividedintomatchedandunmatchedcomponents.Foreachnode, atrackingerrorsystemisestablished,forwhichanIEdrivenbytherelativeoutput measurementsisconstructedtoestimatethesensorfaultsandacombinedsignalof theleader’sinput,processfaults,andmatcheddisturbancecomponent.Basedonthe estimation,afaulttoleranttrackingprotocolisdesignedtoeliminatetheeffectsof thecombined signal.Besides,theeffectofunmatched disturbancecomponent can beattenuatedbydirectlyadjustingsomespecifiedparameters. In Chap. 7, the cooperative tracking control problem for MASs with unknown externaldisturbancesunderadirectedgraphisstudied.Theleader’sinputisnonzero andunavailabletothefollowers.Basedontherelativeoutputmeasurementsofneigh- boring agents, a novel observer-based cooperative tracking protocol is presented, whereagroupofIEsareconstructedtoestimatethetrackingerrorsandthecombined signalofthedisturbancesandtheleader’sinputsimultaneously,thendecentralized trackingprotocolsaredesignedbasedontheobtainedestimates. InChap.8,weproposeanimprovedobserver-basedfault-toleranttrackingcontrol approachforindustrialMASs.Firstly,agroupofnewdistributedIEsarepresented, where the design structure is modified to enhance the feasibility of the estimation scheme. It is shown that the both of the nominal distributed IE and the traditional extendedstateobserver(ESO)arespecialcasesoftheproposedestimator.Secondly, theestimationperformancecanbeimprovedsignificantlyviaanonlinereinforcement Preface vii learningestimationstrategy,whosecoreisanadaptive switchingmechanism inte- gratedwithafunctionblockofsourcefaultmodelocalization.Benefitingfromsatis- factory estimation results, good fault-tolerant tracking control performance can be guaranteeddespiteofmultiplefaultsanddisturbances.Theapplicationtoanetworked multi-axismotioncontrolsystemdemonstratestheeffectivenessandsuperiorityof theproposedmethod. In Chap. 9, the fault reconstruction problem of mobile robots is studied. To be specific,anovelIEisproposedtoreconstructthefaults,wheretheestimationperfor- manceisguaranteedinthesenseofdrivingtheestimationerrorstoasmallprescribed energyboundviaatwo-dimensionalgain-regulationmechanism.Itisshownthatthe proposedestimatorismoreaccuratethantheexistingESOandnominalIE. InChap.10,weconsiderthemultipleattackreconstructionproblemforCPSs.A newprojectedintermediateestimatorisproposed,wherethecomputationcomplexity problem is solved by reducing the number of loop iterations significantly via enhancingthedesignsofloopiteration,terminationconditionandparameterselec- tionstrategy,withoutsacrificingtheattackreconstructionperformance.Compared with traditional IEs, the dependence of linear matrix inequality technique is completelyremoved,besides,theintrinsicheavyovershootingproblemintransient periodiseffectivelyalleviated. Finally,conclusionsandfutureresearchdirectionsarepresentedinChap.11. Hangzhou,China Jun-WeiZhu XinWang Guang-HongYang Acknowledgements ThisworkisdedicatedtomywifeXiao-LingZhouandmyPh.D.studentCao-Yuan Gu. The authors would like to express especial thanks to Prof. Steven X. Ding, oftheInstituteforAutomaticControlandComplexSystems(AKS),Universityof Duisburg-Essen,47057Duisburg,Germanyfortheirvaluablecommentsandencour- agementontheresearchwork.Meanwhile,theauthorswouldliketoacknowledge the support of research grants, including National Natural Science Foundation of China (61803334, 61822311, 61703148, 61673351), Zhejiang Provincial Natural ScienceFoundationofChina(LZ21F030004,LQ18F030012),theStateScholarship FundofChinaScholarshipCouncil(201908330040),NSFC-ZhejiangJointFundfor theIntegrationofIndustrializationandInformatization(U1709213). ix Contents 1 Introduction .................................................. 1 1.1 Background ............................................. 1 1.2 BasicConceptsinFaultDiagnosis .......................... 2 1.3 FEMethodandResearchStatus ............................ 3 1.4 ResearchStatusforFTC .................................. 5 1.5 BookOutline ............................................ 7 2 IEforLipschitzianNonlinearSystems .......................... 11 2.1 Introduction ............................................. 11 2.2 ProblemStatementandPreliminaries ........................ 12 2.3 DesignoftheIE .......................................... 13 2.3.1 TheIEDesignforNonlinearSystemswithSingle Faults ........................................... 13 2.3.2 Extension of IE for Nonlinear Systems withMultipleFaults ............................... 17 2.4 SimulationExample ...................................... 20 2.4.1 ExampleI ....................................... 20 2.4.2 ExampleII ....................................... 21 2.5 Conclusion .............................................. 25 3 IEforUncertainSystems ...................................... 27 3.1 Introduction ............................................. 27 3.2 PreliminariesandProblemStatement ........................ 28 3.3 TheDesignoftheIE-BasedFAStrategy ..................... 29 3.4 Example ................................................ 34 3.4.1 Example1 ....................................... 34 3.4.2 Example2 ....................................... 36 3.5 Conclusion .............................................. 40 xi xii Contents 4 IEforTime-VaryingDelaySystems ............................. 43 4.1 Introduction ............................................. 43 4.2 ProblemStatementandPreliminaries ........................ 44 4.3 IE-BasedFTCScheme .................................... 45 4.4 SimulationExample ...................................... 50 4.5 Conclusion .............................................. 53 5 DistributedIEforComplexNetworks ........................... 55 5.1 Introduction ............................................. 55 5.2 PreliminariesandProblemStatement ........................ 56 5.2.1 BasicGraphTheory ............................... 56 5.2.2 ProblemStatement ................................ 56 5.3 TheDesignoftheDistributedIEs ........................... 57 5.4 SimulationExample ...................................... 64 5.4.1 ExampleI ....................................... 64 5.4.2 ExampleII ....................................... 69 5.5 Conclusion .............................................. 75 6 DistributedIEforMASswithUndirectedGraph ................. 77 6.1 Introduction ............................................. 77 6.2 PreliminariesandProblemStatement ........................ 78 6.2.1 BasicGraphTheory ............................... 78 6.2.2 ProblemStatement ................................ 78 6.3 TheDesignoftheDistributedIEBasedFaultTolerant TrackingProtocol ........................................ 80 6.4 SimulationExample ...................................... 87 6.5 Conclusion .............................................. 95 7 DistributedIEforMASswithDirectedGraph ................... 97 7.1 Introduction ............................................. 97 7.2 PreliminariesandProblemStatement ........................ 98 7.3 TheDesignoftheIE-basedTrackingProtocol ................ 99 7.4 SimulationExample ...................................... 105 7.5 Conclusion .............................................. 109 8 IntelligentIEforMASs ........................................ 111 8.1 Introduction ............................................. 111 8.2 PreliminariesandProblemStatement ........................ 112 8.2.1 GraphTheory .................................... 112 8.2.2 ProblemStatement ................................ 113 8.3 MainResults ............................................ 114 8.3.1 A Novel Observer-based CFTTC Protocol withAdaptiveSwitchingMechanism ................ 114 8.3.2 StabilityAnalysis ................................. 117 8.3.3 CFTTCwithOnlineReinforcementLearning EstimationStrategy ............................... 121